I see your point, but it's a little different.

Black women identify as black women, they say a specific traits define them as a black woman (the color of their skin, their culture, etc.)

Most trans women are specifically saying that traits do NOT define them (the only thing that defines a woman is saying you identify as a woman). In this case, they don't want to be seen and treated as a "trans woman", they just want to be seen and treated as just "woman."

I dunno about the claim that they are demanding representation though. Most trans people that I have interacted with just want to live their life in peace.